Our task is to find out the length and width of the field.
Let the length of the field be L and the width of the field be W
Area of rectangle is given by A=L*B .
Perimeter of rectangle is given by P=2(L+B).
Using information given by the question we have the following 2 equations:
L*B = 300 ......(1)
2(L+B) = 80 ......(2)
Since we have two unknowns and two equations, we can solve the simultaneous equation.
Substitute (3) into (2):
Divide by 2 on both sides:
300/B + B = 40
Multiply by B on both sides:
300 + B^2 = 40B
B^2 -40B + 300 = 0
(B-30)(B-10) = 0
B = 30 or 10
Substitute the values of B into (1), we realise that
If B=30, L=10
If B=10, L=30
Hence the length and breadth are 30cm and 10 cm or vice versa